Literal Inequalities

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SWBAT solve literal inequalities by examining how the individual variables are related to each other.

Big Idea

Solving literal inequalities requires students to reason abstractly about the values of the variables in the inequality.

Warm Up

10 minutes

This warm-up activity should be completed in pairs.  While students are working, I will circulate around the room and work with students who I observed to be having difficulty solving literal equations in yesterday's lesson.  As students are finishing, I will select students to post solution on the board so they can be discussed with the entire class.


10 minutes

During this section of the lesson, I will use the Literal_Inequalities_Launch presentation to guide a class discussion.

Slide 2

I let students try this series of questions with their partner.  Students will have to make a plan for solving this inequality and determine if their plan makes sense.  I will encourage students to consider whether they can begin by solving the inequality in the same way they would solve an equation.  Part 2 will allow students to connect this abstract concept (solving a literal inequality) to a more concrete concept of plugging in values.  Part 3 will pull everything together for students showing them that the solutions are the same.

Teaching Point: I encourage my students to continue to justify their steps when solving an inequality.  When you discuss the question as a class, revisit the properties from solving inequalities such as if a<b then a + c < b + c.

Slides 3-5

In slides 3-5, I will really push my students to reason abstractly about inequalities.  The idea that the value of the inequality can change based on the relative values of the variables is important. Some students will struggle with this concept because of the abstract nature (e.g. a>b).  If students are struggling you can always have them plug in real values to see how the solution works out.

Slide 3

For this task I will have students do a around Question 1.  If necessary, I will go back to the idea of solving the inequality -2x > 8 without dividing by a negative number (add 2x to both sides first). This will help students remember why the inequality reverses directions when dividing or multiplying by a negative number.

Slide 4

I usually give my students a few minutes to think about this next question but we usually end up going over it as a class.  When students are working, listen for good starter ideas and then go back to these students during the whole-class discussion.  The idea of conditions (example a > b or a < b) will be important during the practice portion of the lesson.  With this in mind, make sure you are guiding students towards understanding about why these conditions are important.

Slide 5

This question will lead into the practice portion of the lesson.  Have students attempt this problem with their partner.  Remind them that the solution can be found in two different ways (dividing by a first, or distributing the a)  Have two students show the two different methods on the board so that the class can see an example of the method that they did not try.**


**As an alternative you could also have all students solve the inequality using both methods and then show that when the numbers are substituted in the solution is the same.


15 minutes

I have students work in pairs on Literal_Inequalities_Practice.  Students should be discussing and comparing solutions.  Students should also be able to validate their solutions to the various inequalities.  Some of this validation is built in to the questions such as in 3b and 3c.

This practice assignment continues to challenge students with their abstract reasoning.  The first three questions require students to practice with solving and justifying their steps.  They will also need to reason about how certain values within the inequality effect the overall solution.  In questions 4-8, students will continue to investigate how the conditions given of the relative size of variables within the inequality determine the overall solution.   


5 minutes

This Closing Activity requires students to put the ideas from the practice into their own words.  In order to solve the inequality correctly the relationship between r and b needs to be known. Students will be describing how this relationship between r and b will effect the solution.  Most students will focus on the cases where either r > b or r < b, however, some may discuss r = b.  As students are writing, try to eavesdrop on their thoughts.  If time permits, let students turn and talk with their partner about what they wrote and then have a class share-out trying to get students who had particularly interesting ideas to share their thoughts (MP3).